{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from neural_odes import *\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve the Discrete Lotka-Volterra Eqtn for general non-symmetric $A$\n",
    "\\begin{equation}\n",
    "    \\begin{aligned}\n",
    "    p_i(t+1) &= p_i(t)\\big[1+r_i\\big(1-\\frac{\\sum_{j=1}^dA_{ij}p_j(t)}{k_i}\\big)\\big], i = 1, \\dots d\\\\\n",
    "    &= p_i(t)\\big[1+r_i\\big(1-\\frac{\\mathbf{b}_i^T\\big(\\sum_{j=1}^d\\mathbf{c}_jp_j(t)\\big)}{k_i}\\big)\\big], i = 1, \\dots d \\\\\n",
    "    &= p_i(t)\\big[1+r_i\\big(1-\\frac{\\mathbf{b}_i^TC\\mathbf{p}}{k_i}\\big)\\big], i = 1, \\dots d \\\\\n",
    "    \\end{aligned}\n",
    "\\end{equation}."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We approximate $A_{ij} = \\mathbf{b}_i^T\\mathbf{c}_j$ using the low rank matrix approximation $A= B^TC$, where $B = [\\mathbf{b}_1, \\cdots, \\mathbf{b}_d] \\in \\mathbb{R}^{k \\times d}$ and $C = [\\mathbf{c}_1, \\cdots, \\mathbf{c}_d] \\in \\mathbb{R}^{k \\times d}$.  Each $\\mathbf{b}_i, \\mathbf{c}_i \\in \\mathbb{R}^k$, where $k \\ll d$ are the embeddings of time series $i$.\n",
    "\n",
    "In matrix-vector form, we have $A\\mathbf{p}$, which has computational complexity $\\mathcal{O}(d^2)$ for $A \\in \\mathbb{R}^{d \\times d}, \\mathbf{p} \\in \\mathbb{R}^d$.  Using the low-rank form, we can write $A\\mathbf{p} = B^T(C \\mathbf{p})$.  We do not want to explicitly form the matrix $B^TC$, since this would have higher complexity of $\\mathcal{O}(kd^2)$.  We instead break the computation into two matrix-vector products as indicated by the parathesis, each of complexity $\\mathcal{O}(kd) \\ll \\mathcal{O}(d^2).$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start with $d = 100$ for the number of time series and will learn the synthetic data from the equation for random initialized $A, \\mathbf{r}, \\mathbf{k}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 0. Set parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_time_series = 100\n",
    "num_time_steps = 10\n",
    "low_rank_param = 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To enable the symmetric form, where $C = B$, set `is_sym = True`.\n",
    "\n",
    "To explicitly form the low rank matrix matrix product $A = B^TC$, set `is_full_matrix = True`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "is_sym = False\n",
    "is_full_matrix = False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1. Generate data for $A \\in \\mathbb{R}^{d \\times d}, \\mathbf{r}, \\mathbf{k} \\in \\mathbb{R}^d$ and the initial condition $\\mathbf{p}(0) \\in \\mathbb{R}^d$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use gpu and higher precision for numerical computations\n",
    "ctx = mx.gpu()\n",
    "dtype = \"float64\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100,), (100,), (100,), (100, 100))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_, _, p0, A = generate_data(num_time_series)\n",
    "r = nd.ones(num_time_series, ctx=ctx, dtype=dtype)\n",
    "k = 100 * r\n",
    "r.shape, k.shape, p0.shape, A.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3. Solve the LV eqn for $p_i(t+1), 0 \\le t < N - 1$.  We store $P$ as a matrix in $\\mathbb{R}^{d \\times N}$, whose first column is the initial condition $\\mathbf{p}(0) \\in \\mathbb{R}^d$. Then $P = [\\mathbf{p}(0), \\dots, \\mathbf{p}(N-1)].$  Use two embeddings to learn $B, C \\in \\mathbb{R}^{k \\times d}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "neural_lv = NeuralLV(\n",
    "    num_time_series,\n",
    "    num_time_steps,\n",
    "    low_rank_param,\n",
    "    is_full_matrix,\n",
    "    p0,\n",
    "    r,\n",
    "    k,\n",
    "    A,\n",
    "    is_sym,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set number of iterations to run\n",
    "num_epochs = 5000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8bba2582e384413482319751e4c09338",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=5000), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "p_approx, p, A_approx, model = neural_lv.run(num_epochs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5165dee831154bf498a15f21706faa0e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=1000), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# Can re run until convergence extra 1000 at a time (Ran twice for total of 7000 iterations)\n",
    "p_approx, p, A_approx, model = neural_lv.run(model=model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 5. Error Evaluation and Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l2 norm of the error = \n",
      "[0.08958898]\n",
      "<NDArray 1 @gpu(0)>\n"
     ]
    }
   ],
   "source": [
    "print(f\"l2 norm of the error = {nd.norm(p_approx-p)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "max norm of the error = \n",
      "[0.01711842]\n",
      "<NDArray 1 @gpu(0)>\n"
     ]
    }
   ],
   "source": [
    "print(f\"max norm of the error = {nd.max(nd.abs(p_approx-p))}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l2 matrix norm of the error of A and its low rank approx = \n",
      "[39.32629733]\n",
      "<NDArray 1 @gpu(0)>\n"
     ]
    }
   ],
   "source": [
    "print(\n",
    "    \"l2 matrix norm of the error of A and its low rank approx =\"\n",
    "    f\" {nd.norm(A_approx-A)}\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# First ten time series\n",
    "lv_plot_ts(p, p_approx, fig_size_width=20)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "conda_mxnet_p36",
   "language": "python",
   "name": "conda_mxnet_p36"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
